A gas kinetic algorithm for flows in microchannel

A gas-kinetic numerical algorithm using the molecular velocity distribution function equation is developed and extended to solve the gas flows in micro-channels. Based on the kinetic Shakhov model, the velocity distribution function equation is used to describe the micro-scale gas flows with various Knudsen numbers. The gas-kinetic finite difference scheme based on the unsteady time-splitting technique is constructed to directly solve the discrete velocity distribution functions. The numerical modeling of the gas kinetic boundary conditions is presented. The numerical integration method for the discrete velocity space is developed to evaluate the macroscopic flow parameters at each point in the physical space. To verify the present method, the classical Couette flows with various Knudsen numbers, the pressure-driven Poiseuille flow in two-dimensional short micro-channel are simulated and compared with the approximate solutions of the linearized Boltzmann equation.